Geodesic webs on a two-dimensional manifold and Euler equations

Document Type

Article

Publication Date

1-1-2010

Abstract

We prove that any planar 4-web defines a unique projective structure in the plane in such a way that the leaves of the web foliations are geodesics of this projective structure. We also find conditions for the projective structure mentioned above to contain an affine symmetric connection, and conditions for a planar 4-web to be equivalent to a geodesic 4-web on an affine symmetric surface. Similar results are obtained for planar d-webs, d>4, provided that additional d-4 second-order invariants vanish. © 2009 Springer Science+Business Media B.V.

Identifier

73849103573 (Scopus)

Publication Title

Acta Applicandae Mathematicae

External Full Text Location

https://doi.org/10.1007/s10440-009-9437-1

e-ISSN

15729036

ISSN

01678019

First Page

5

Last Page

17

Issue

1

Volume

109

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